Definition 2.2 
Let \(\mathcal {A}\)  be an abelian category and \(\mathcal {X}\)  be a subcategory of \(\mathcal {A}\) . For a positive integer \(k\)  we denote by \(\mathcal {X}^{{\bot }_k}\)  the full subcategory of \(\mathcal {A}\)  defined by \(\mathcal {X}^{{\bot }_k} = \lbrace A \in \mathcal {A} | \operatorname{Ext}^{0,...,k}(\mathcal {X}, A) = 0\rbrace \) . \(^{{\bot }_k}\mathcal {X}\)  is defined similarly [1]}. Note that by Theorem REF  for a Serre subcategory \(\mathcal {C}\)  of \(\mathcal {A}\)  we have \(\mathcal {C}^{{\bot }_1}=\mathcal {C}^{\bot }\) .

